Abstract

In the field of photogrammetry, computer vision and robotics recursive estimation of time dependent processes is an important task. Usually Kalman filter based techniques are used which rely on explicit model functions that directly and explicitly describe the effect of the parameters on the observations. However, some problems naturally result in implicit constraints between the observations and the parameters, for instance all those resulting in homogeneous equation systems. By implicit we mean that the constraints are given by equations that are not easily solvable for the observation vector. We propose an iterative extended Kalman filter based on implicit measurement equations. The derived filter is useful for various applications, where the possibility to use implicit constraints simplifies the modeling. As an extension, we introduce a robustification technique similar to TrNG et al. (2007) and HUBER (1981) which down-weights the influence of potential outliers. The feasibility of the proposed framework is demonstrated at a number of typical computer vision applications.